CN103489212A - Two-dimensional shape corresponding method based on user inspiration - Google Patents

Two-dimensional shape corresponding method based on user inspiration Download PDF

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CN103489212A
CN103489212A CN201310420958.1A CN201310420958A CN103489212A CN 103489212 A CN103489212 A CN 103489212A CN 201310420958 A CN201310420958 A CN 201310420958A CN 103489212 A CN103489212 A CN 103489212A
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dimensional shapes
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CN103489212B (en
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杨文武
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Zhejiang Outuo Electrical Co ltd
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Zhejiang Gongshang University
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Abstract

The invention discloses a two-dimensional shape corresponding method based on user inspiration. From the aspect of two sets of given two-dimensional shapes, one or more pairs of corresponding relations between the two sets of two-dimensional shapes are specified by a user first, and the corresponding relations between other unspecified two-dimensional shapes between the two sets of two-dimensional shapes are further established by using an algorithm. According to the two-dimensional shape corresponding method based on the user inspiration, the corresponding relations between the two sets of shapes are allowed to be controlled by the user, and only a small amount of user interaction is needed so that the shape corresponding result capable of 'meeting user needs' can be generated. The two-dimensional shape corresponding method based on the user inspiration has the advantages of being small in user interaction amount, high in corresponding efficiency, simple, accurate and efficient in algorithm, capable of correcting errors easily, and simple in coding.

Description

The two-dimensional shapes corresponding method inspired based on the user
Technical field
The present invention relates to the corresponding technical field of two-dimensional shapes, relate in particular to a kind of two-dimensional shapes corresponding method inspired based on the user.
Background technology
Under the active support of the government, domestic animation industry development in recent years is rapid, and animation output also significantly promotes.Yet traditional Freehandhand-drawing 2 D animation needs a large amount of Production Times and great number cost of manufacture.For the aided two-dimensional cartoon making, many two-dimension cartoon making business softwares have been researched and developed both at home and abroad, such as Adobe Flash, Toon Boom Studio etc.These business softwares have mainly realized so-called " paperless cartoon " function, drawing on traditional animation teacher paper are transferred to and allow the animation teacher paint on computers by Digitizing plate, with editor and the management that facilitates cartoon material.But the animation teacher still needs to draw one by one the 2 D animation sequence, workload is still very huge.
Therefore, research and develop intelligentized 2 D animation technology, automatically to generate the 2 D animation sequence, thereby effectively improve the make efficiency of 2 D animation and reduce its cost of manufacture, there is real society and economic implications.
The two-dimensional shapes interpolation is an important technology in the computer animation field, is widely used in two-dimentional key frame vector animation system.This technology can realize in adjacent key frame comprise role's attitude smooth transition, thereby automatically generate the role animation sequence between key frame.In actual two-dimensional vector animation, role's attitude is meaned to form by one group of (a plurality of) two-dimensional shapes usually, and each shape correspondence role's a feature.For the smooth transition between two groups of shapes that realize meaning adjacent two role's attitudes, the two-dimensional shapes interpositioning need to solve a basic problem: the feature on associated two role's attitudes how, how to set up two groups of one-to-one relationships between shape.When drawing role's attitude, the animation teacher can be by draw the upper corresponding shape of each feature of role according to a definite sequence, automatically to realize the shape correspondence between adjacent role's attitude.But this will greatly limit animation teacher's freedom of creation, final impact creation efficiency and quality.A kind of simple effective method is to allow the user specify to set up two groups of correspondences between shape by craft, but this needs more man-machine interactively, thereby has reduced make efficiency.Although people have proposed some automatic shape corresponding method, these methods can not guarantee to produce the corresponding result of shape of " meeting user's needs ", still need more manual interaction to correct result.Therefore, how to reduce the man-machine interactively amount and guarantee that producing correct corresponding result is the problem that the two-dimensional shapes corresponding method is needed solution badly.
China Patent Publication No. CN101903908A, open day is on Dec 01st, 2010, discloses a kind of 2D/3D image registration based on feature.It comprises following methods: property detector, and it is configured for from two dimensional image and extracts the two dimensional character collection, from 3-D view, extracts the three-dimensional feature collection; The projection process device, it is configured for three-dimensional data is projected into to two-dimensional projection data; And registration processor, it is configured for regulates parameter so that described two dimensional character collection and the described three-dimensional feature collection by the projection of described projection process device use perspective geometry are carried out to registration, and the parameter of use through regulating is to be used the described 3-D view of described perspective geometry projection to carry out registration by described two dimensional image with by described projection process device.Weak point is, this 2D/3D method for registering images based on feature, when the feature set correspondence makes a mistake, the projection process device can not be corrected its corresponding mistake, can not adopt algorithm to carry out the Automatic-searching coupling to its corresponding mistake, thereby it is not high to mate corresponding accuracy.
Summary of the invention
The present invention is the deficiency that interactive quantity is large, error correction is difficult, the Corresponding matching accuracy is not high existed in existing complete manual or fully automatic two-dimensional shapes corresponding method in order to solve, provide a kind of precisely efficient, error correction is easy, coding is simple, efficiently a kind of two-dimensional shapes corresponding method inspired based on the user of algorithm.
To achieve these goals, the present invention is by the following technical solutions:
A kind of two-dimensional shapes corresponding method inspired based on the user, comprise the steps:
(1-1) role's attitude of setting in the two-dimensional vector animation is comprised of one group of two-dimensional shapes, and each two-dimensional shapes is corresponding with a role characteristic; The user specifies two role's attitudes
Figure BDA0000382348430000031
with
Figure BDA0000382348430000032
at least one pair of corresponding relation between interior two-dimensional shapes;
(1-2) according to following step, set up
Figure BDA0000382348430000033
connection layout G 1, set up
Figure BDA0000382348430000034
connection layout G 2:
Set G 1in arbitrary summit
Figure BDA00003823484300000318
corresponding
Figure BDA0000382348430000036
in the two-dimensional shapes of
Figure BDA0000382348430000037
set G 2in arbitrary summit
Figure BDA0000382348430000038
corresponding
Figure BDA0000382348430000039
in a two-dimensional shapes
Figure BDA00003823484300000310
set
Figure BDA00003823484300000311
the fillet threshold value be L 1, set
Figure BDA00003823484300000312
the fillet threshold value be L 2;
G 1by following step, set up: work as G 1in the distance of two corresponding two-dimensional shapes in any summit be less than L 1the time, between described two any summits, set up a fillet;
G 2by following step, set up: work as G 2in the distance of two corresponding two-dimensional shapes in any summit be less than L 2the time, between described two any summits, set up a fillet;
(1-3) utilize following algorithm to set up
Figure BDA00003823484300000313
with
Figure BDA00003823484300000314
one-to-one relationship between interior two-dimensional shapes:
(1-3-1) set two shapes
Figure BDA00003823484300000315
with
Figure BDA00003823484300000316
between the similarity measurement scaling function be
f ( S i 1 , S j 2 ) = D L ( S i 1 , S j 2 ) × D O ( S i 1 , S j 2 ) × D A ( S i 1 , S j 2 ) ;
Figure BDA0000382348430000041
Figure BDA0000382348430000042
Figure BDA0000382348430000043
Wherein,
Figure BDA0000382348430000044
be respectively two-dimensional shapes
Figure BDA0000382348430000045
size, towards and outward appearance; be respectively two-dimensional shapes
Figure BDA0000382348430000047
size, towards and outward appearance;
(1-3-2) specified every pair of two-dimensional shapes of corresponding relation for the user, at connection layout G 1and G 2middlely finding out respectively this to the corresponding summit of shape, is a pair of associated summit pair by this to apex marker;
(1-3-3) set G 1and G 2in arbitraryly to incident vertex, to comprised summit, be:
Figure BDA0000382348430000048
with
Figure BDA0000382348430000049
wherein, be positioned at G 1in,
Figure BDA00003823484300000411
be positioned at G 2in; Will
Figure BDA00003823484300000412
with
Figure BDA00003823484300000413
adjacent vertex in not yet associated summit put into respectively set P and Q;
(1-3-4) will gather any summit in P
Figure BDA00003823484300000414
with any summit in Q
Figure BDA00003823484300000415
be associated, form a pair of candidate association summit pair, utilize the similarity measurement scaling function to calculate
Figure BDA00003823484300000416
with
Figure BDA00003823484300000417
the degree of association
Figure BDA00003823484300000418
wherein, for
Figure BDA00003823484300000420
corresponding shape,
Figure BDA00003823484300000421
for
Figure BDA00003823484300000422
corresponding shape;
(1-3-5) when the candidate association summit is greater than zero to number, choose all degrees of association
Figure BDA00003823484300000423
in maximal value will corresponding candidate association summit is to being labeled as associated summit pair, and this summit to corresponding two shape correspondences together; Return to step (1-3-3);
When equalling zero to number in the candidate association summit, G 1and G 2correspondence between the corresponding two groups of shapes in middle summit completes.
The two-dimensional shapes interpolation is an important technology in the computer animation field, is widely used in two-dimentional key frame vector animation system.This technology can realize in adjacent key frame comprise role's attitude smooth transition, thereby automatically generate the role animation sequence between key frame.
For solve in adjacent key frame comprise role's attitude the smooth transition problem, need to be at first by two role's attitudes of the same role of adjacent key frame
Figure BDA0000382348430000051
with
Figure BDA0000382348430000052
one-to-one relationship between interior two-dimensional shapes.
The problem to be solved in the present invention is exactly how efficiently and exactly to set up two groups of corresponding relations between shape.
The two-dimensional shapes corresponding method inspired based on the user of the present invention is from two groups of given two-dimensional shapes, at first the user specifies one or more pairs of corresponding relations between two groups of two-dimensional shapes, and uses algorithm is further set up the corresponding relation between other unspecified two-dimensional shapes between two groups of two-dimensional shapes.Method of the present invention allows the user to control two groups of corresponding relations between shape, and only needs a small amount of user interactions can produce the corresponding result of shape of " meeting user's needs ".The present invention has solved the correspondence problem between two groups of two-dimensional shapes effectively, can be efficiently and set up exactly corresponding relation between any two groups of shapes.
As preferably, in step (1-2), also comprise the steps:
The curve of described any two corresponding two-dimensional shapes in summit is carried out respectively discrete, calculate the mean place of all discrete points of every curve, mean place is made as to the center of gravity of corresponding two-dimensional shapes;
Calculate the distance between the center of gravity of described any two corresponding two-dimensional shapes in summit, the distance between the center of gravity of two-dimensional shapes is made as to the distance between two-dimensional shapes;
Select
Figure BDA0000382348430000053
in arbitrary two-dimensional shapes, calculate described two-dimensional shapes and arrive
Figure BDA0000382348430000054
in the distance of other two-dimensional shapes, the mean value of getting each distance is fillet threshold value L 1;
Select
Figure BDA0000382348430000061
in arbitrary two-dimensional shapes, calculate described two-dimensional shapes and arrive
Figure BDA0000382348430000062
in the distance of other two-dimensional shapes, the mean value of getting each distance is fillet threshold value L 2.
As preferably, described
Figure BDA0000382348430000063
for two-dimensional shapes
Figure BDA0000382348430000064
total arc length; Described
Figure BDA0000382348430000065
for initial point arrives two-dimensional shapes
Figure BDA0000382348430000066
the vector that forms of center of gravity and the angle of forward x axle;
Figure BDA0000382348430000067
for two-dimensional shapes
Figure BDA0000382348430000068
on the number of vision significance point.
As preferably, described
Figure BDA0000382348430000069
for two-dimensional shapes
Figure BDA00003823484300000610
total arc length;
Figure BDA00003823484300000611
for initial point arrives shape
Figure BDA00003823484300000612
the vector that forms of center of gravity and the angle of forward x axle; for shape
Figure BDA00003823484300000614
the number of upper vision significance point.
As preferably, described conspicuousness point comprises point with extreme curvature and end points.
The present invention can reach following effect: (1) amount of user interaction is little, and corresponding efficiency is high; (2) algorithm is simple, accurate, efficient, and error correction is easy, and coding is simple.
The accompanying drawing explanation
Fig. 1 is a kind of process flow diagram of embodiments of the invention;
Fig. 2 is two two-dimensional character attitudes of the present invention
Figure BDA00003823484300000615
with
Figure BDA00003823484300000616
Fig. 3 of the present inventionly specifies two two-dimensional character attitudes after a pair of shape corresponding relation by the user
Figure BDA00003823484300000617
with
Fig. 4 is two the corresponding two-dimensional attitude figure that complete of the present invention.
In figure: role's attitude role's attitude
Figure BDA00003823484300000620
fillet 3.
Embodiment
Embodiment as shown in Figure 1 is a kind of two-dimensional shapes corresponding method inspired based on the user, comprises the steps:
Step 100, role's attitude of setting in the two-dimensional vector animation is comprised of one group of two-dimensional shapes, and as shown in Figure 2, each two-dimensional shapes is corresponding with a role characteristic; As shown in Figure 3, the user specifies two role's attitudes
Figure BDA0000382348430000071
with
Figure BDA0000382348430000072
a pair of corresponding relation 3 between interior two-dimensional shapes;
Step 200, set up according to following step
Figure BDA0000382348430000073
connection layout G 1, set up
Figure BDA0000382348430000074
connection layout G 2:
Set G 1in arbitrary summit
Figure BDA0000382348430000075
corresponding
Figure BDA0000382348430000076
in the two-dimensional shapes of
Figure BDA0000382348430000077
; Set G 2in arbitrary summit
Figure BDA0000382348430000078
corresponding
Figure BDA0000382348430000079
in a two-dimensional shapes
Figure BDA00003823484300000710
; Set
Figure BDA00003823484300000711
the fillet threshold value be L 1, set
Figure BDA00003823484300000712
the fillet threshold value be L 2;
G 1by following step, set up: work as G 1in the distance of two corresponding two-dimensional shapes in any summit be less than L 1the time, between described two any summits, set up a fillet;
G 2by following step, set up: work as G 2in the distance of two corresponding two-dimensional shapes in any summit be less than L 2the time, between described two any summits, set up a fillet;
In the present embodiment, the curve of described any two corresponding two-dimensional shapes in summit is carried out respectively discrete, calculate the mean place of all discrete points of every curve, mean place is made as to the center of gravity of corresponding two-dimensional shapes;
Calculate the distance between the center of gravity of described any two corresponding two-dimensional shapes in summit, the distance between the center of gravity of two-dimensional shapes is made as to the distance between two-dimensional shapes;
Select in arbitrary two-dimensional shapes, calculate described two-dimensional shapes and arrive in the distance of other two-dimensional shapes, the mean value of getting each distance is fillet threshold value L 1;
Select
Figure BDA00003823484300000715
in arbitrary two-dimensional shapes, calculate described two-dimensional shapes and arrive
Figure BDA00003823484300000716
in the distance of other two-dimensional shapes, the mean value of getting each distance is fillet threshold value L 2.
Step 300, utilize following algorithm to set up
Figure BDA0000382348430000081
with
Figure BDA0000382348430000082
one-to-one relationship between interior two-dimensional shapes:
Step 301, set two shapes
Figure BDA0000382348430000083
with
Figure BDA0000382348430000085
between the similarity measurement scaling function be
f ( S i 1 , S j 2 ) = D L ( S i 1 , S j 2 ) × D O ( S i 1 , S j 2 ) × D A ( S i 1 , S j 2 ) ;
Figure BDA0000382348430000087
Figure BDA0000382348430000088
Figure BDA0000382348430000089
Wherein,
Figure BDA00003823484300000810
be respectively two-dimensional shapes
Figure BDA00003823484300000811
size, towards and outward appearance; be respectively two-dimensional shapes
Figure BDA00003823484300000813
size, towards and outward appearance;
Figure BDA00003823484300000814
for two-dimensional shapes total arc length; Described
Figure BDA00003823484300000816
for initial point arrives two-dimensional shapes the vector that forms of center of gravity and the angle of forward x axle;
Figure BDA00003823484300000818
for two-dimensional shapes
Figure BDA00003823484300000819
on the number of vision significance point.
Figure BDA00003823484300000820
for two-dimensional shapes
Figure BDA00003823484300000821
total arc length;
Figure BDA00003823484300000822
for initial point arrives shape
Figure BDA00003823484300000823
the vector that forms of center of gravity and the angle of forward x axle;
Figure BDA00003823484300000824
for shape
Figure BDA00003823484300000825
the number of upper vision significance point.The conspicuousness point comprises point with extreme curvature and end points.
Step 302, specified every pair of two-dimensional shapes of corresponding relation, at connection layout G for the user 1and G 2middlely finding out respectively this to the corresponding summit of shape, is a pair of associated summit pair by this to apex marker;
Step 303, set G 1and G 2in arbitraryly to incident vertex, to comprised summit, be:
Figure BDA00003823484300000826
with
Figure BDA00003823484300000827
wherein,
Figure BDA00003823484300000828
be positioned at G 1in,
Figure BDA00003823484300000829
be positioned at G 2in; Will
Figure BDA00003823484300000830
with
Figure BDA00003823484300000831
adjacent vertex in not yet associated summit put into respectively set P and Q;
Step 304, by any summit in set P
Figure BDA0000382348430000091
with any summit in Q
Figure BDA0000382348430000092
be associated, form a pair of candidate association summit pair, utilize the similarity measurement scaling function to calculate
Figure BDA0000382348430000093
with
Figure BDA0000382348430000094
the degree of association
Figure BDA0000382348430000095
wherein,
Figure BDA0000382348430000096
for
Figure BDA0000382348430000097
corresponding shape,
Figure BDA0000382348430000098
for
Figure BDA0000382348430000099
corresponding shape;
Step 305, when the candidate association summit is greater than zero to number, choose all degrees of association
Figure BDA00003823484300000910
in maximal value
Figure BDA00003823484300000911
will
Figure BDA00003823484300000912
corresponding candidate association summit is to being labeled as associated summit pair, and this summit to corresponding two shape correspondences together; Return to step 303;
As shown in Figure 4, when equalling zero to number in the candidate association summit, G 1and G 2correspondence between the corresponding two groups of shapes in middle summit completes.
Should be understood that the present embodiment only is not used in and limits the scope of the invention for the present invention is described.Should be understood that in addition those skilled in the art can make various changes or modifications the present invention after the content of having read the present invention's instruction, these equivalent form of values fall within the application's appended claims limited range equally.

Claims (5)

1. the two-dimensional shapes corresponding method inspired based on the user, is characterized in that, comprises the steps:
(1-1) role's attitude of setting in the two-dimensional vector animation is comprised of one group of two-dimensional shapes, and each two-dimensional shapes is corresponding with a role characteristic; The user specifies two role's attitudes
Figure FDA0000382348420000011
with
Figure FDA0000382348420000012
at least one pair of corresponding relation between interior two-dimensional shapes;
(1-2) according to following step, set up connection layout G 1, set up
Figure FDA0000382348420000014
connection layout G 2.
Set G 1in arbitrary summit corresponding
Figure FDA0000382348420000016
in the two-dimensional shapes of
Figure FDA0000382348420000017
set G 2in arbitrary summit
Figure FDA0000382348420000018
corresponding
Figure FDA0000382348420000019
in a two-dimensional shapes
Figure FDA00003823484200000110
set
Figure FDA00003823484200000111
the fillet threshold value be L 1, set
Figure FDA00003823484200000112
the fillet threshold value be L 2;
G 1by following step, set up: work as G 1in the distance of two corresponding two-dimensional shapes in any summit be less than L 1the time, between described two any summits, set up a fillet;
G 2by following step, set up: work as G 2in the distance of two corresponding two-dimensional shapes in any summit be less than L 2the time, between described two any summits, set up a fillet;
(1-3) utilize following algorithm to set up
Figure FDA00003823484200000113
with
Figure FDA00003823484200000114
one-to-one relationship between interior two-dimensional shapes:
(1-3-1) set two shapes
Figure FDA00003823484200000115
with
Figure FDA00003823484200000116
between the similarity measurement scaling function be
f ( S i 1 , S j 2 ) = D L ( S i 1 , S j 2 ) × D O ( S i 1 , S j 2 ) × D A ( S i 1 , S j 2 ) ;
Figure FDA00003823484200000119
Wherein,
Figure FDA0000382348420000022
be respectively two-dimensional shapes
Figure FDA0000382348420000023
size, towards and outward appearance; be respectively two-dimensional shapes
Figure FDA0000382348420000025
size, towards and outward appearance;
(1-3-2) specified every pair of two-dimensional shapes of corresponding relation for the user, at connection layout G 1and G 2middlely finding out respectively this to the corresponding summit of shape, is a pair of associated summit pair by this to apex marker;
(1-3-3) set G 1and G 2in arbitraryly to incident vertex, to comprised summit, be:
Figure FDA0000382348420000026
with
Figure FDA0000382348420000027
wherein,
Figure FDA0000382348420000028
be positioned at G 1in, be positioned at G 2in; Will with
Figure FDA00003823484200000211
adjacent vertex in not yet associated summit put into respectively set P and Q;
(1-3-4) will gather any summit in P
Figure FDA00003823484200000212
with any summit in Q
Figure FDA00003823484200000213
be associated, form a pair of candidate association summit pair, utilize the similarity measurement scaling function to calculate
Figure FDA00003823484200000214
with
Figure FDA00003823484200000215
the degree of association
Figure FDA00003823484200000216
wherein,
Figure FDA00003823484200000217
for
Figure FDA00003823484200000218
corresponding shape,
Figure FDA00003823484200000219
for
Figure FDA00003823484200000220
corresponding shape;
(1-3-5) when the candidate association summit is greater than zero to number, choose all degrees of association
Figure FDA00003823484200000221
in maximal value
Figure FDA00003823484200000222
will
Figure FDA00003823484200000223
corresponding candidate association summit is to being labeled as associated summit pair, and this summit to corresponding two shape correspondences together; Return to step (1-3-3);
When equalling zero to number in the candidate association summit, G 1and G 2correspondence between the corresponding two groups of shapes in middle summit completes.
2. the two-dimensional shapes corresponding method inspired based on the user according to claim 1, is characterized in that, in step (1-2), also comprises the steps:
The curve of described any two corresponding two-dimensional shapes in summit is carried out respectively discrete, calculate the mean place of all discrete points of every curve, mean place is made as to the center of gravity of corresponding two-dimensional shapes;
Calculate the distance between the center of gravity of described any two corresponding two-dimensional shapes in summit, the distance between the center of gravity of two-dimensional shapes is made as to the distance between two-dimensional shapes;
Select
Figure FDA0000382348420000031
in arbitrary two-dimensional shapes, calculate described two-dimensional shapes and arrive
Figure FDA0000382348420000032
in the distance of other two-dimensional shapes, the mean value of getting each distance is fillet threshold value L 1;
Select
Figure FDA0000382348420000033
in arbitrary two-dimensional shapes, calculate described two-dimensional shapes and arrive
Figure FDA0000382348420000034
in the distance of other two-dimensional shapes, the mean value of getting each distance is fillet threshold value L 2.
3. the two-dimensional shapes corresponding method inspired based on the user according to claim 1, is characterized in that, described
Figure FDA0000382348420000035
for two-dimensional shapes
Figure FDA0000382348420000036
total arc length; Described
Figure FDA0000382348420000037
for initial point arrives two-dimensional shapes the vector that forms of center of gravity and the angle of forward x axle;
Figure FDA0000382348420000039
for two-dimensional shapes
Figure FDA00003823484200000310
on the number of vision significance point.
4. the two-dimensional shapes corresponding method inspired based on the user according to claim 1, is characterized in that, described
Figure FDA00003823484200000311
for two-dimensional shapes
Figure FDA00003823484200000312
total arc length; for initial point arrives shape the vector that forms of center of gravity and the angle of forward x axle;
Figure FDA00003823484200000315
for shape the number of upper vision significance point.
5. according to the described two-dimensional shapes corresponding method inspired based on the user of claim 3 or 4, it is characterized in that, described conspicuousness point comprises point with extreme curvature and end points.
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杨文武，冯结青，王勋: "基于多层次特征结构的二维形状渐变", 《计算机辅助设计与图形学学报》 *
杨文武，冯结青，金小刚，彭群生: "基于特征分解的2-D多边形渐变", 《软件学报》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104424658A (en) * 2014-10-22 2015-03-18 浙江工商大学 Structure-preserving interpolation method of two-dimensional shapes
CN104424658B (en) * 2014-10-22 2017-09-29 浙江工商大学 A kind of two-dimensional shapes interpolating method of structure-preserving
CN107633543A (en) * 2017-08-21 2018-01-26 浙江工商大学 Consider the stripe shape corresponding method of local topology
CN107633543B (en) * 2017-08-21 2020-12-08 浙江工商大学 Line shape corresponding method considering local topological structure
CN107978010A (en) * 2017-11-27 2018-05-01 浙江工商大学 Accurate shape matching process stage by stage
CN107978010B (en) * 2017-11-27 2021-03-05 浙江工商大学 Staged precise shape matching method

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